This is the first volume of a work envisioned to consist of six volumes, providing a complete overview of the unified approach to basic problems of linguistics, as developed by Hans-Heinrich Lieb. This first volume contains a detailed overview of Integrational Linguistics, and outlines a major fragment of a theory of language systems. The further volumes will discuss: II. A theory of grammars; III. Language universals and language contrast; IV. Syntax and semantics; V. Morphology and morphosemantics; VI. Lexical semantics.